This paper is motivated by major needs for accurate on-line state estimation (SE) in the emerging electrical energy systems; accurate state and topology are needed to support operator's decisions as system conditions vary both during normal conditions for enhanced efficiency and during contingency conditions to ensure reliable operations. We propose a new SE method which is based on a combined use of informative historical data with the extended state space formulation for managing the nonlinear nature of AC power flow equations and related numerical problems. Specifically, the approach comprises two stages. First, based on historical data maximum-likelihood parameter estimation is conducted to update model parameters. The second stage utilizes these estimated model parameters and on-line measurements to estimate the state. Instead of using the extended Kalman Filter we are using a Kalman Filter in a model-based physically meaningful kernel feature space. This leads to ax two-stage Kalman Filter which can overcome problems created by the occasional missing data or data available at different rates (SCADA and PMU data); therefore, we claim that its performance is highly robust. This claim is confirmed by the simulation results performed for several IEEE test systems which show significant improvements over the performance of both the static SE with Newton's method and the extended Kalman Filter SE approach; once the parameters are learned, the computational time is smaller than the currently used SE, making it feasible in operations.
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